Suppose the points are and . Since is not in the Poincaré universe, the points , and are distinct. The Möbius circle through , and is perpendicular to the edge, since it contains a pair of inverse points, so there is at least one line through , and . Furthermore, any Möbius circle through and perpendicular to the edge must also contain , and so coincides with the first circle. Thus there is at most one line through and .